Monatshefte für Mathematik最新文献

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On lattice extensions 关于晶格扩展
Monatshefte für Mathematik Pub Date : 2024-01-27 DOI: 10.1007/s00605-023-01935-x
Maxwell Forst, Lenny Fukshansky
{"title":"On lattice extensions","authors":"Maxwell Forst, Lenny Fukshansky","doi":"10.1007/s00605-023-01935-x","DOIUrl":"https://doi.org/10.1007/s00605-023-01935-x","url":null,"abstract":"<p>A lattice <span>(Lambda )</span> is said to be an extension of a sublattice <i>L</i> of smaller rank if <i>L</i> is equal to the intersection of <span>(Lambda )</span> with the subspace spanned by <i>L</i>. The goal of this paper is to initiate a systematic study of the geometry of lattice extensions. We start by proving the existence of a small-determinant extension of a given lattice, and then look at successive minima and covering radius. To this end, we investigate extensions (within an ambient lattice) preserving the successive minima of the given lattice, as well as extensions preserving the covering radius. We also exhibit some interesting arithmetic properties of deep holes of planar lattices.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wave-breaking and persistence properties in weighted $$L^p$$ spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities 具有二次和三次非线性的卡马萨-霍姆型方程在加权$L^p$$$空间中的破波和持久特性
Monatshefte für Mathematik Pub Date : 2024-01-25 DOI: 10.1007/s00605-023-01938-8
Wenguang Cheng, Ji Lin
{"title":"Wave-breaking and persistence properties in weighted $$L^p$$ spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities","authors":"Wenguang Cheng, Ji Lin","doi":"10.1007/s00605-023-01938-8","DOIUrl":"https://doi.org/10.1007/s00605-023-01938-8","url":null,"abstract":"<p>We consider the Cauchy problem of a Camassa–Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted <span>(L^p)</span> spaces.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"215 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Groups in which all involutions are 3-transvections 所有渐开线都是 3 变换的群
Monatshefte für Mathematik Pub Date : 2024-01-25 DOI: 10.1007/s00605-023-01941-z
Egle Bettio, Enrico Jabara
{"title":"Groups in which all involutions are 3-transvections","authors":"Egle Bettio, Enrico Jabara","doi":"10.1007/s00605-023-01941-z","DOIUrl":"https://doi.org/10.1007/s00605-023-01941-z","url":null,"abstract":"<p>Let <i>G</i> be a group which is generated by the set of its involutions, and assume that the set of integers which occur as orders of products of two involutions in <i>G</i> is <span>({1,2,3,4})</span>. It is shown that <span>(Gsimeq textrm{PSL}(2,7))</span> or <span>(Gsimeq textrm{PSU}(3,3))</span> or <i>G</i> is a <span>({2,3})</span>-group and <span>(G/O_{2}(G) simeq S_{3})</span>.\u0000</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A sharp two-weight estimate for the maximal operator under a bump condition 凹凸条件下最大算子的尖锐两重估计值
Monatshefte für Mathematik Pub Date : 2024-01-24 DOI: 10.1007/s00605-023-01932-0
Adam Osękowski
{"title":"A sharp two-weight estimate for the maximal operator under a bump condition","authors":"Adam Osękowski","doi":"10.1007/s00605-023-01932-0","DOIUrl":"https://doi.org/10.1007/s00605-023-01932-0","url":null,"abstract":"<p>Let <span>({mathcal {M}}_{mathcal {D}})</span> be the dyadic maximal operator on <span>({mathbb {R}}^n)</span>. The paper contains the identification of the best constant in the two-weight estimate </p><span>$$begin{aligned} Vert {mathcal {M}}_{mathcal {D}}fVert _{L^p(w)}le C_{p,sigma ,w}Vert fVert _{L^p(sigma ^{1-p})} end{aligned}$$</span><p>under the assumption that the pair <span>((sigma ,w))</span> of weights satisfies an appropriate bump condition. The result is shown to be true in the larger context of abstract probability spaces equipped with a tree-like structure.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the deductive strength of the Erdős–Dushnik–Miller theorem and two order-theoretic principles 关于厄尔多斯-杜什尼克-米勒定理的演绎强度和两个秩序理论原则
Monatshefte für Mathematik Pub Date : 2024-01-24 DOI: 10.1007/s00605-023-01933-z
Eleftherios Tachtsis
{"title":"On the deductive strength of the Erdős–Dushnik–Miller theorem and two order-theoretic principles","authors":"Eleftherios Tachtsis","doi":"10.1007/s00605-023-01933-z","DOIUrl":"https://doi.org/10.1007/s00605-023-01933-z","url":null,"abstract":"<p>We provide answers to open questions from Banerjee and Gopaulsingh (Bull Pol Acad Sci Math 71: 1–21, 2023) about the relationship between the Erdős–Dushnik–Miller theorem (<span>(textsf{EDM})</span>) and certain weaker forms of the Axiom of Choice (<span>(textsf{AC})</span>), and we properly strengthen some results from Banerjee and Gopaulsingh (2023). We also settle a part of an open question of Lajos Soukup (stated in Banerjee and Gopaulsingh (2023) [Question 6.1]) about the relationship between the following two order-theoretic principles, which [as shown in Banerjee and Gopaulsingh (2023)] are weaker than <span>(textsf{EDM})</span>: (a) “Every partially ordered set such that all of its antichains are finite and all of its chains are countable is countable” (this is known as Kurepa’s theorem), and (b) “Every partially ordered set such that all of its antichains are countable and all of its chains are finite is countable”. In particular, we prove that (b) does not imply (a) in <span>(textsf{ZF})</span> (i.e., Zermelo–Fraenkel set theory without <span>(textsf{AC})</span>). Moreover, with respect to (b), we answer an open question from Banerjee and Gopaulsingh (2023) about its relationship with the following weak choice form: “Every set is either well orderable or has an amorphous subset”; in particular, we show that (b) follows from, but does not imply, the latter weak choice principle in <span>(textsf{ZFA})</span> (i.e., Zermelo–Fraenkel set theory with atoms).</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform density topology 均匀密度拓扑
Monatshefte für Mathematik Pub Date : 2024-01-24 DOI: 10.1007/s00605-023-01929-9
{"title":"Uniform density topology","authors":"","doi":"10.1007/s00605-023-01929-9","DOIUrl":"https://doi.org/10.1007/s00605-023-01929-9","url":null,"abstract":"<h3>Abstract</h3> <p>Main results of the paper are: the Lebesgue Density Theorem does not hold for the uniform density points and the uniform density topology is completely regular. </p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"162 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some special subspaces of a Banach space, from the perspective of best coapproximation 从最佳协同逼近的角度看巴拿赫空间的某些特殊子空间
Monatshefte für Mathematik Pub Date : 2024-01-23 DOI: 10.1007/s00605-023-01930-2
{"title":"On some special subspaces of a Banach space, from the perspective of best coapproximation","authors":"","doi":"10.1007/s00605-023-01930-2","DOIUrl":"https://doi.org/10.1007/s00605-023-01930-2","url":null,"abstract":"<h3>Abstract</h3> <p>We study the best coapproximation problem in Banach spaces, by using Birkhoff–James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obtain a necessary condition for the strongly anti-coproximinal subspaces in a reflexive Banach space whose dual space satisfies the Kadets–Klee Property. On the other hand, we provide a sufficient condition for the strongly anti-coproximinal subspaces in a general Banach space. We also characterize the anti-coproximinal subspaces of a smooth Banach space. Further, we study these special subspaces in a finite-dimensional polyhedral Banach space and find some interesting geometric structures associated with them.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"117 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On spectral measures and convergence rates in von Neumann’s Ergodic theorem 论冯-诺依曼遍历定理中的谱量和收敛率
Monatshefte für Mathematik Pub Date : 2024-01-22 DOI: 10.1007/s00605-023-01928-w
{"title":"On spectral measures and convergence rates in von Neumann’s Ergodic theorem","authors":"","doi":"10.1007/s00605-023-01928-w","DOIUrl":"https://doi.org/10.1007/s00605-023-01928-w","url":null,"abstract":"<h3>Abstract</h3> <p>We show that the power-law decay exponents in von Neumann’s Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value 1. In this work we also prove that, under an assumption of weak convergence, in the absence of a spectral gap, the convergence rates of the time-average in von Neumann’s Ergodic Theorem depend on sequences of time going to infinity.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit 卡马萨-霍尔姆方程零滤波极限解的非均匀收敛性
Monatshefte für Mathematik Pub Date : 2024-01-22 DOI: 10.1007/s00605-023-01931-1
Jinlu Li, Yanghai Yu, Weipeng Zhu
{"title":"Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit","authors":"Jinlu Li, Yanghai Yu, Weipeng Zhu","doi":"10.1007/s00605-023-01931-1","DOIUrl":"https://doi.org/10.1007/s00605-023-01931-1","url":null,"abstract":"<p>In this short note, we prove that given initial data <span>(u_0in H^s(mathbb {R}))</span> with <span>(s&gt;frac{3}{2})</span> and for some <span>(T&gt;0)</span>, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in <span>(L^infty (0,T;H^s(mathbb {R})))</span> to the inviscid Burgers equation as the filter parameter <span>(alpha )</span> tends to zero. This is a complement of our recent result on the zero-filter limit.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"41 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A central limit theorem for integer partitions into small powers 将整数分割为小幂的中心极限定理
Monatshefte für Mathematik Pub Date : 2023-12-15 DOI: 10.1007/s00605-023-01926-y
Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy
{"title":"A central limit theorem for integer partitions into small powers","authors":"Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy","doi":"10.1007/s00605-023-01926-y","DOIUrl":"https://doi.org/10.1007/s00605-023-01926-y","url":null,"abstract":"<p>The study of the well-known partition function <i>p</i>(<i>n</i>) counting the number of solutions to <span>(n = a_{1} + dots + a_{ell })</span> with integers <span>(1 le a_{1} le dots le a_{ell })</span> has a long history in number theory and combinatorics. In this paper, we study a variant, namely partitions of integers into </p><span>$$begin{aligned} n=leftlfloor a_1^alpha rightrfloor +cdots +leftlfloor a_ell ^alpha rightrfloor end{aligned}$$</span><p>with <span>(1le a_1&lt; cdots &lt; a_ell )</span> and some fixed <span>(0&lt; alpha &lt; 1)</span>. In particular, we prove a central limit theorem for the number of summands in such partitions, using the saddle-point method.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138683477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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